International audienceWe present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it
We present TRIQS/CTHYB, a state-of-the art open-source implementation of the continuoustime hybridisation expansion quantum impurity solver of the TRIQS package. This code is mainly designed to be used with the TRIQS library in order to solve the self-consistent quantum impurity problem in a multi-orbital dynamical mean field theory approach to strongly-correlated electrons, in particular in the context of realistic calculations. It is implemented in C++ for efficiency and is provided with a high-level Python interface. The code is ships with a new partitioning algorithm that divides the local Hilbert space without any user knowledge of the symmetries and quantum numbers of the Hamiltonian. Furthermore, we implement higher-order configuration moves and show that such moves are necessary to ensure ergodicity of the Monte Carlo in common Hamiltonians even without symmetry-breaking. PROGRAM SUMMARY
Problems of finite temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise representation of these functions. In this paper, we explore the representation of Green's functions and self-energies in terms of series of Chebyshev polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev representation for realistic systems with the uniform-power grid representation, which is most commonly used in this context. arXiv:1805.03521v2 [cond-mat.stat-mech]
We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real-time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo methods have now reached a state where they can be used as dynamical mean field impurity solvers and the dynamical sign problem can be overcome. As non-equilibrium problems can be simulated at the same cost, we envisage the main use of these methods as dynamical mean field solvers for time-dependent problems far from equilibrium.
We analyze the time-dependent formation of the spectral function of an Anderson impurity model in the Kondo regime within a numerically exact real-time quantum Monte Carlo framework. At steady state, splitting of the Kondo peak occurs with nontrivial dependence on voltage and temperature, and with little effect on the location or intensity of high-energy features. Examining the transient development of the Kondo peak after a quench from an initially uncorrelated state reveals a two-stage process where the initial formation of a single central Kondo peak is followed by splitting. We analyze the time dependence of splitting in detail and demonstrate a strong dependence of its characteristic timescale on the voltage. We expect both the steady state and the transient phenomenon to be experimentally observable.Introduction. Interacting quantum many-body systems often exhibit highly entangled states that cannot be described within an independent particle formalism. The Kondo effect in a quantum dot 1,2 coupled to noninteracting leads is the paradigmatic example for such a state, as the dot electrons hybridize with the leads to form a highly correlated Kondo singlet state 3 . This state manifests itself as a sharp peak in the local density of states 2,4 . The establishment of Kondo correlations can be examined in a quantum quench scenario, where an initially uncorrelated state slowly develops a coherence peak over time 5,6 .In the presence of a voltage, the Kondo peak is strongly suppressed and splits into two smaller peaks 7-11 . Previous work has argued that the peak-to-peak distance is given by the voltage 12-17 and that the split state is significantly less correlated than the equilibrium state 12 . It is therefore natural to examine the establishment of splitting after a quench from an initially uncorrelated state, and to expect that this less correlated state forms on a timescale shorter than that of the equilibrium state.Despite significant analytical progress 18-24 , an accurate investigation of this scenario requires numerical methods that are able to simulate the real-time evolution after a quench accurately, for times long enough to reach the steady state. Additionally, a full account of the continuous lead spectrum is crucial for correct treatment of the nonequilibrium steady state. The major families of numerical methods include the noncrossing approximation and its higher-order generalizations 25 , wavefunction-based methods 26-31 , real-time path integral techniques 32-35 , the time-dependent numerical renormalization group 36-40 , hierarchical equations of motion 41-44 , the auxiliary master equation approach 45-49 , and a wide variety of quantum Monte Carlo methods 50-66 . Most of these approaches fall short in at least one of the aforementioned requirements. This situation has changed with the development of the numerically exact inchworm quantum Monte Carlo method 67-71 that in many cases eliminates the dynamical sign problem and is thereby able to reach the relevant timescales.
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